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math.OC2018
On principal frequencies and inradius in convex sets
Lorenzo Brasco
We generalize to the case of the Laplacian an old result by Hersch and Protter. Namely, we show that it is possible to estimate from below the first eigenvalue of the Dirichlet…
math.OC2018
On principal frequencies and isoperimetric ratios in convex sets
Lorenzo Brasco
On a convex set, we prove that the Poincaré-Sobolev constant for functions vanishing at the boundary can be bounded from above by the ratio between the perimeter and a suitable pow…